You will need to get a visa in order to do an internship in Singapore. For this, you will first need to procure either a letter of invitation from a company, or a document stating an agreement between your home university or business/engineering school and a university in Singapore . This will in turn get you a student's pass.
There are many big European, Australian & American companies that offer internships in their Singapore branches or with a partner company. Companies such as Carrefour, Renault, Agilent, Ernst & Young, HSBC and many others are helpful in helping people find internships with them.
Another avenue to explore in your search would be to contact the embassy or consulate of your country in Singapore to see what they have to offer.
The following links may be useful in looking for internships:
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